Graphing Logarithmic Functions

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Show your work for each problem.

1.
What is the domain of $y = \log_3 x$ ?
1. a) $x > 3$
2. b) $x \geq 0$
3. c) $x > 0$
4. d) $x < 0$
2.
The point $(8, y)$ lies on the graph of $y = \log_2 x$ . What is $y$ ?
3.
Complete the table of values for $y = \log_3 x$ at $x = \frac{1}{3}, 1, 3, 9$ .
4.
What is the vertical asymptote of $y = \log_2(x + 4)$ ?
1. a) $x = -4$
2. b) $x = 4$
3. c) $y = 0$
4. d) $y = -4$
5.
At which $x$ does the graph of $y = \log_5 x$ cross the $x$ -axis?
6.
The point $(2, 9)$ lies on $y = 3^x$ . Find the matching point on $y = \log_3 x$ .
7.
Which function has a decreasing graph?
1. a) $y = \ln x$
2. b) $y = \log_5 x$
3. c) $y = \log_{10} x$
4. d) $y = \log_{1/3} x$
8.
The graph of $y = \log_3(x - 7) + 2$ has the vertical asymptote $x = c$ . What is $c$ ?
9.
Graph $y = \log_2(x - 5)$ : find the asymptote and two key points.
10.
On the graph of $y = \log_{1/2} x$ , how much does $y$ change when $x$ goes from $\frac{1}{2}$ to $4$ ?
11.
The graph of $y = \log_4 x$ is the reflection across the line $y = x$ of which graph?
1. a) $y = 4x$
2. b) $y = 4^x$
3. c) $y = x^4$
4. d) $y = \frac{x}{4}$
12.
What is $y$ on the graph of $y = \log_2(x + 1) - 3$ at $x = 7$ ?
13.
The graph of $y = \log_2 x$ is shifted to $y = \log_2(x + 3) - 4$ . Where do the key points $(1, 0)$ and $(2, 1)$ go?
14.
Which function has the vertical asymptote $x = 2$ and passes through $(3, -1)$ ?
1. a) $y = \log_2(x - 2) + 1$
2. b) $y = \log_2(x - 2) - 1$
3. c) $y = \log_2(x + 2) - 1$
4. d) $y = \log_2(x - 1) - 1$
15.
Find the $x$ -intercept of $y = \log_3(x - 1) - 2$ . Enter the value of $x$ .
16.
Graph $y = -\log_3(x + 2)$ : find the asymptote, the $x$ -intercept and two more points.
17.
A graph $y = \log_b(x - h) + k$ has the asymptote $x = 1$ and passes through $(2, 3)$ and $(6, 4)$ . Find $h$ , $k$ and $b$ .
18.
Study $y = \log_2(6 - 2x)$ : find the asymptote, one point and the $x$ -intercept.